Objects, properties and relations

Ontology, the theory of being or existence, is centrally concerned with the question "What is there? What exists?". One tempting response to this question is that things exist. This leads to the indubitably true but ultimately useless answer, "Everything exists". Progress can be made when we begin to ask the further question "What kinds of things exist?". This requires us to think about what sorts of things there are. An immediate distinction we can make is between objects and properties. Loosely speaking, the distinction corresponds roughly (and only roughly) to the grammatical distinction between the subject and the predicate of a sentence. For example, the sentence "John is tall" has grammatical subject "John" and predicate "is tall", and is about the object John and the property of being tall. The sentence says that the object John possesses the property of being tall.

Below, some technical terminology concerning objects, properties and relations and some further distinctions will be introduced. The aim is simply to familiarize you with the terminology itself, not to settle any philosophical controversies. Let us here, however, briefly consider a problem from the philosophy of mind—the mind/body problem—as an illustration of how these distinctions are relevant. What is it to have a mind? How am I capable of having conscious experiences, swings of mood, rational beliefs, and trains of thought? And how are these phenomena related to my body and my bodily states, especially the state of my brain and central nervous system? Descartes thought that the essence of all mental phenomena was their relationship to consciousness. The essence of all physical phenomena, the human body included, however, was to be extended in space. Descartes believed that he had thus individuated two distinct substances, or types of object, for something could clearly be an item in my consciousness without having any spatial properties whatsoever, and something could be located in space without bearing any relation to consciousness whatsoever. For Descartes, then, a person is a union of two distinct objects, a physical body and an immaterial mind.

Recent critics of the Cartesian conception of the mind have argued that it rests upon a fundamental misconception. It conceives of the mind as an object, when in fact it is not one. Rather, to have a mind is simply to have or be capable of having mental characteristics or properties. A person is a single object, but one which has or is capable of having various properties, including the properties of having toothache, being anxious, believing that the Earth revolves around the Sun, and solving a crossword clue. The issue now is what is the relationship between these characteristically mental properties and other, physical, properties, such as being in some brain state or other. Are the former explainable in terms of the latter?


As long as we are thinking of physical things the idea of what an object is, and the distinction between objects and properties, seem obvious. But are there objects which are not physical, and which are not located spatially, and which do not endure in time? For instance, many philosophers believe that numbers are objects. They are not supposed to be the kinds of objects which one can bump into, or which came into existence at some particular time, however. Rather they are thought to be abstract objects, which are neither located in space or time.

Earlier, it was claimed that the ontological category "object" roughly corresponds to that which is picked out by the grammatical category of "subject". The analogy between object and property, and subject and predicate, begins to break down however when we notice that not only can we truly say "Pillar boxes are red", but also "Red is a colour". For in the first sentence "red" occurs as part of the predicate, and in the second it occurs as the subject. So is red an object or a property? We can solve this dilemma by distinguishing between universals and particulars. Red is a property of individual, physical objects, and such objects are said to possess the property, or alternatively the property is said to inhere in them. These objects are called particulars. Furthermore, we can talk about the property itself, in abstraction from any particular instantiation of it. When we talk of the property in this way, we are discussing a universal. Some philosophers believe that universals have a distinct existence, distinct that is from any particular instantiation. In such a case, universals would themselves be (rather confusingly) objects, although objects of a quite different ontological category to the particulars which instantiate the universal. That is there would be the particular objects which possess the property red, and the universal object redness.

Another important distinction is that between tokens and types. A particular red object is a token of the type "red objects". The distinction is useful when it is unclear whether one is talking about a particular instance of something or the general type. For instance, consider the question "How many letter are there in the word 'balloon'?". If we mean token letters, then there are seven. But if we mean letter types then there are five: "a", "b", "l", "n" and "o". We say that the two "l"s in "balloon" are two tokens of the same type.


Perhaps one of the most important distinctions to be drawn is that between an object's essential and accidental properties. In metaphysics we are concerned to understand the fundamental nature of things. We want to know what it is about something that makes it the thing it is. An object's essential properties are those properties which it could not lack. For instance, imagine a glass of pure, distilled water. Now we could easily imagine that this self same sample of water could have been in a mug and not a glass. It might have been at a different place. It could have been a different temperature to the temperature it actually is. But it could not have been made up of anything other than H2O molecules. For that is what water is. Being composed of H2O molecules is an essential property of water, it is what it is for something to be water. Being a particular temperature, or in one container or another, or one location or another, are accidental properties of the sample of water. It could have lacked those properties without ceasing to be what it is.

By treating objects and properties as basic ontological categories we can perhaps explain another important ontological category—events—in terms of them. An event is when something occurs or changes, either instantaneously (as in a flash of lightening), or over some duration of time (as in a boulder rolling down a hill). An event, it seems, can be explained as the instantiation or uninstantiation (or both) of some property or properties by some object at some particular time (or during some interval) and at some particular place.

A further distinction to be drawn is that between intrinsic and extrinsic properties. Consider an imaginary person, John. Let us say that John is 5'10" tall, that he weighs 10 stone, has blue eyes and brown hair, and is loved by Mary, is taller than James, and is the PhD student of Prof. Smith. Then his intrinsic properties include being 5'10" tall, weighing 10 stone, having blue eyes and having brown hair. His extrinsic properties include being loved by Mary, being taller than James, and being Prof. Smith's PhD student. The reason the former are intrinsic properties of John's is that they are dependent solely upon his nature, upon his make-up. The latter are extrinsic properties of John's because they are determined partially by other particulars such as Mary, James and Prof. Smith, and John's relation to them. For instance whether or not John has the extrinsic property of being taller than James depends not only on one of John's intrinsic properties (namely John's height), but also on one of James' intrinsic properties (James' height). Normally, when we talk of an object's properties we mean its intrinsic properties. Extrinsic properties are normally talked of in terms of relations holding between two or more particular objects.


Finally, we will consider the different categories of relations, and their logical properties. In the following definitions will be provided informally in ordinary English, followed by an example.


A relation R is transitive if and only if (henceforth abbreviated "iff"),
if x is related by R to y, and y is related by R to z, then x is related by R to z.

For example, "being taller than" is a transitive relation: if John is taller than Bill, and Bill is taller than Fred, then it is a logical consequence that John is taller than Fred.

A relation R is intransitive iff,
if x is related by R to y, and y is related by R to z, then x is not related by R to z.

For example, "being next in line to" is an intransitive relation: if John is next in line to Bill, and Bill is next in line to Fred, then it is a logical consequence that John is not next in line to Fred.

A relation R is non-transitive iff it is neither transitive nor intransitive.

For example, "likes" is a non-transitive relation: if John likes Bill, and Bill likes Fred, there is no logical consequence concerning John liking Fred.


A relation R is symmetric iff,
if x is related by R to y, then y is related by R to x.

For example, "being a cousin of" is a symmetric relation: if John is a cousin of Bill, then it is a logical consequence that Bill is a cousin of John.

A relation R is asymmetric iff,
if x is related by R to y, then y is not related by R to x.

For example, "being the father of" is an asymmetric relation: if John is the father of Bill, then it is a logical consequence that Bill is not the father of John.

A relation R is non-symmetric iff it is neither symmetric nor asymmetric.

For example, "loves" is a non-symmetric relation: if John loves Mary, then, alas, there is no logical consequence concerning Mary loving John.


A relation R is reflexive iff,
everything bears R to itself.

For example, "being the same height as" is a reflexive relation: everything is the same height as itself.

A relation R is irreflexive iff,
nothing bears R to itself.

For example, "being taller than" is an irreflexive relation: nothing is taller than itself.

A relation R is non-reflexive iff it is neither reflexive nor irreflexive.

For example, "loves" is a non-reflexive relation: there is no logical reason to infer that somebody loves themselves or does not love themselves.


A relation R is an equivalence relation or a congruence relation iff R is transitive, symmetric and reflexive.

For example, "identical" is an equivalence relation: if x is identical to y, and y is identical to z, then x is identical to z; if x is identical to y then y is identical to x; and x is identical to x.

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